Question

For the circuit above, vi(t) = 6cos(2π900t). The output voltage
is in this form: vo = |vo|6cos(2π900t + φ). You will observe that
both |vo| and φ depend on the frequency of vi. Derive the
expressions for the ratio |vo/vi| and φ as functions of
frequency.

I found |vo| = 1.223 and φ = -14.8834 for this circuit. Now, I'm
confused how to go about deriving the equations as function of
frequency. I used the equations I calculated for vi(t) and vo(t) to
find the ratio of them in terms of frequency, which came out to be
1.223cos(2πft - 14.883), and now I can't solve a general equation
for φ without having to know vo and vi, which doesn't seem
right.

Please thoroughly explain your reasoning for deriving the
function of φ in terms of frequency.